Halbach Permanent Magnet Array Research Articles

Semi‐interior permanent‐magnet actuators for high‐magnet‐utilisation and low‐cost applications

Generally, for small- and medium-sized tubular permanent-magnet (PM) linear actuators, PM structures can be divided into two categories. One is interior PM (IPM) structure and the other is surface-mounted PM (SPM), involving a compromise between flux per pole and magnet leakage flux. This study proposes a novel semi-IPM (s-IPM) structure for a tubular linear actuator having the advantages of high flux per pole of IPM and small magnet leakage flux of SPM. The air-gap flux density and the average thrust are analysed and compared with IPM and SPM by the magnetic equivalent circuit and finite element analysis. Moreover, the s-IPM structure is also compared with Halbach PM array in terms of the average thrust and the magnet utilisation. Four prototype actuators with different PM structures are built and tested. Both the theoretical and experimental results show that the magnet utilisation of the s-IPM structure is the largest while its cost and volume are approximately unchanged. The proposed s-IPM actuators are of great prominence in high-magnet-utilisation and low-cost applications.

Improvement of Tubular Permanent Magnet Machine Performance Using Dual-Segment Halbach Array

In this paper, a modification of the dual-segment permanent magnet (PM) Halbach array is investigated to improve the performance of the tubular linear machine, in terms of flux density and output power. Instead of a classical Halbach array with only radial and axial PMs, the proposed model involves the insertion of mig-magnets, which have a magnetized angle shifted from the reference magnetized angles of axial and radial PMs. This structure leads to the elimination of flux leakage and the concentration of flux linkage in middle of the coil; therefore, the output power is increased by 13.2%.

Design and Analysis of Halbach Ironless Flywheel BLDC Motor/Generators

Halbach array-based permanent magnet (PM) brushless machines exhibit attractive features when compared with conventional PM brushless machines with normal segmented magnets, including the flux-concentration effect, essentially sinusoidal air-gap flux density due to PMs, and negligible cogging torque. However, as for a motor/generator used in flywheel, an external rotor composed of Halbach array and rotor back-iron is necessary to increase the inertia of flywheel system, which is different from the conventional external-rotor machines. In this paper, a Halbach array PM motor is studied compared with the radial magnet array. The relationship between the air-gap field distribution and the magnet array is discussed. Finally, the eddy current loss in PMs of the external-rotor ironless brushless dc motor is analyzed between the Halbach PM motor and the conventional PM motor.

Microwave probe stations with three-dimensional control of the magnetic field to study high-frequency dynamics in nanoscale devices.

We present two microwave probe stations with motorized rotary stages for adjusting the magnitude and angle of the applied magnetic field. In the first system, the magnetic field is provided by an electromagnet and can be adjusted from 0 to ∼1.4 T while its polar angle (θ) can be varied from 0° to 360°. In the second system, the magnetic field is provided by a Halbach array permanent magnet, which can be rotated and translated to cover the full range of polar (θ) and azimuthal (φ) angles with a tunable field magnitude up to ∼1 T. Both systems are equipped with microwave probes, bias-Ts, amplifiers, and spectrum analyzers to allow for microwave characterization up to 40 GHz, as well as software to automatically perform continuous large sets of electrical and microwave measurements.

End-Effect Magnetic Field Analysis of the Halbach Array Permanent Magnet Spherical Motor

The Halbach array permanent magnet (PM) spherical motor (PMSM) consists of a spherical rotor and a spherical-shell stator. The magnetic field distribution surrounding the rotor PMs is closely related to the spherical structure of the Halbach array PMSM. The Halbach array PM configuration characteristics lead to the end leakage magnetic field in the latitudinal direction of the spherical structure, which is end effect. Establishment of an accurate 3-D magnetic field analytical model containing the end leakage magnetic field of the Halbach array PMSM is the foundation of magnetic field distortion research with its influence on eddy-current loss. The magnetic field distribution of the Halbach array PMs in the air gap is calculated using the scalar magnetic potential. Laplace and Poisson equations of the scalar magnetic potential in the spherical coordinate system are derived. To analyze the end leakage magnetic field of the Halbach array PMSM in the latitudinal direction, concept of mechanical pseudo-cycle in the motor latitudinal direction is proposed, and the cycle of Fourier series is redefined. A completed 3-D analytical expression of the Halbach array PMSM magnetic field distribution is derived by the new Fourier series and spatial integral technology, in which the end leakage magnetic field is contained. The results obtained by the proposed analytical method are compared with the numerical results, i.e., the results obtained by the finite-element method, which verify the effectiveness of the analytical method. Magnetic field distribution containing the end leakage magnetic field in different magnetization methods is compared and analyzed, which shows that the Halbach array magnetization has a larger main air-gap magnetic field and a smaller end leakage magnetic field. The effect of motor structure parameters on the end leakage magnetic field is analyzed, and the effect of end leakage magnetic field on eddy-current loss is preliminarily discussed, which shows that eddy-current loss caused by end effect almost accounts for half of the total eddy-current loss. The research on end effect and the effect of motor parameters on end effect are of great significance. In the end, the leakage magnetic field results obtained by the proposed analytical method are verified by the experimental results.

Analytical modelling of Halbach linear generator incorporating pole shifting and piece-wise spring for ocean wave energy harvesting

Halbach permanent magnet (PM) array has attracted tremendous research attention in the development of electromagnetic generators for its unique properties. This paper has proposed a generalized analytical model for linear generators. The slotted stator pole-shifting and implementation of Halbach array have been combined for the first time. Initially, the magnetization components of the Halbach array have been determined using Fourier decomposition. Then, based on the magnetic scalar potential method, the magnetic field distribution has been derived employing specially treated boundary conditions. FEM analysis has been conducted to verify the analytical model. A slotted linear PM generator with Halbach PM has been constructed to validate the model and further improved using piece-wise springs to trigger full range reciprocating motion. A dynamic model has been developed to characterize the dynamic behavior of the slider. This analytical method provides an effective tool in development and optimization of Halbach PM generator. The experimental results indicate that piece-wise springs can be employed to improve generator performance under low excitation frequency.

Characteristics investigation of single-sided ironless pmlsm based on halbach array for medium-speed Maglev train

This paper investigates characteristics of ironless permanent magnet linear synchronous motor (PMLSM) based on Halbach array used for medium-speed (200km/h) maglev train. Long primary ironless coil is laid in the middle of track and the Halbach permanent magnet array is attached to the bottom of each bogie as a source of traction, U-shape electromagnets at the both sides of the train for levitation. Two dimensional analytical model of single-sided ironless PMLSM based on Halbach array is established, using linear overlay method, the no-load air gap magnetic field is calculated firstly, winding current density distribution is obtained for calculating the characteristics of thrust and normal force against power angle, including force characteristics with equal and unequal pole pitch, the influence of steel sleeper, etc. Besides, the mathematical model for this type motor is built by 3D finite element method, the traction characteristics of medium-speed maglev under maximum speed 200km/h are calculated. The characteristics of this type motor are satisfactory owing to there is no detent force in the motor and thrust force reach maximum meanwhile normal force can be eliminated. Calculation method is verified by comparing finite element results, experimental result on a 200kW type motor further validates the accuracy of calculation and some important conclusions are obtained.

Mechanical Design Considerations of an “Ironless,” High-Specific-Power Electric Machine

This paper describes the mechanical design considerations for a 1 MW, 14 000 rpm motor which achieves a specific power of at least 13 kW/kg. This is enabled through an “ironless,” inside out, Halbach array permanent magnet, high frequency, and airgap or slotless configuration. The “ironless” design creates mechanical challenges because thin radial builds which reduce weight also typically reduce structural stability and vibrational damping. Structural deformation challenges include radial expansion and static bending. Vibrational issues include stator resonance mode excitation as well as rotor dynamic resonance excitation. The mechanical challenges were studied with analytical calculations and high-fidelity finite-element analysis. These analyses drove design refinements to mitigate these challenges. The rotor has then been tested to verify these analysis results.

Research on a PM Slotless Linear Generator Based on Magnet Field Analysis Model for Wave Energy Conversion

In this paper, a permanent magnet (PM) slotless tubular linear generator based on magnet field analysis model is presented for wave energy conversion. To improve air flux density and efficiency of the generator, two improved Halbach PM Arrays (T-PM structure and claw-PM structure) applied in the slotless linear generator is proposed and compared with Halbach PM Arrays. Combined with axisymmetric dimensional finite-element method (FEM), no-load electromagnetic performance is analyzed. Finally, due to test and analysis model results of prototype concordant with the FEM results, the generator model and the analysis method are correct.

A Novel Linear Permanent Magnet Vernier Machine With Consequent-Pole Permanent Magnets and Halbach Permanent Magnet Arrays

The linear permanent magnet (PM) vernier machine (LPMVM) can reach a higher thrust density at low speed compared to the regular linear PM machines due to the utilization of the magnetic gear effect, which makes it a good solution for low-speed direct-drive applications. In order to further improve the machine thrust density, a novel LPMVM with consequent-pole and Halbach PM array is proposed and optimized in this paper. Then, in order to show the superior thrust performance of the proposed LPMVM, it is compared to two conventional LPMVMs in terms of back electric motive force (back EMF), thrust force, and power factor. It is found that machine no-load back EMF can be improved by 72.5% and its thrust density is 46% higher than that of the conventional LPMVM.

Analysis of Half Halbach Array Configurations in Linear Permanent-Magnet Vernier Machine

Due to the high efficiency, high force capability and low cost, the linear permanent-magnet (PM) vernier (LPMV) machine is very suitable for long stroke applications such as urban rail transits. This paper proposes the LPMV machines with various topologies of half Halbach PM array, and investigates their electromagnetic performances, such as back electromotive force, force capability, PM eddy current loss and iron loss. Firstly, the configuration and operation principle of the LPMV machines are presented. By using the finite element method, it can be known that the LPMV machine with half Halbach PM array in the armature core exhibits high thrust and low detent force. Then, the demagnetizations of half PM array are analyzed to guarantee the security and credibility of the machine in operation. Finally, the effectiveness of the theoretical analysis is validated by the experiments on a prototype of the LPMV machine.

Design and Analysis of Counter-Rotating Dual Rotors Permanent Magnet Compensated Pulsed Alternator

This paper presents the methodology for the electromagnetic design and analysis of air-cored pulsed alternators, which is based on a new type counter-rotating dual rotor permanent magnet compensated pulsed alternator (CRDR-PMCPA). The application of the CRDR topology in the field of CPA is used to decrease the large transient torque transmitted to the combat vehicle platform. Based on the air-cored structures and the pulse operation duty, the special design flowchart was presented. Halbach array permanent magnet rotors were designed for using the characteristic of unilateral magnetism gathering in the CRDR-PMCPA. The parameters of the air-cored dual rotors pulsed alternators were calculated and compared by the analytical method and finite-element analysis (FEA) method (FEM). The inductance of the armature winding is important for obtaining the pulsed current waveform accurately. The inductance of the armature winding is calculated by the numerical method and FEM, respectively. The mechanical design of the CRDR-PMCPA was done. The transient discharge process was simulated in detail for evaluating the design performance, and the operation risks of permanent magnets were also evaluated. The special problems for dual rotors rotating were investigated. The electromagnetic design and analysis is the base for accurately calculating the transient thermal rise and mechanical impulse aspects. Thermal and structural analysis was done by the multiphysics coupling analysis. And the results were used to evaluate the demagnetization risk of permanent magnets and evaluate the safety of the whole machine and the discharge system.

Octagonal Halbach Magnet Array Design for a Magnetic Refrigerator

ABSTRACTAn effective magnet array design for magnetic refrigeration systems is crucial given the space limitations and need for maintaining the required cooling capacity. Here, Halbach permanent magnet arrays (HPMA) in an octagonal orientation are studied using NdFeB permanent magnets. Gadolinium is selected as the magnetocaloric material (MCM) for the aperture inside the octagonal HPMA. The optimum outer-to-inner radii ratio for the octagonal HPMA and MCM system is found to be 2, at which the cooling energy per volume of magnet has a peak. For this ratio, the effect of using soft magnetic material, which in this study is FeVCo, inside and outside the HPMA is evaluated over a range of material thicknesses. The optimum soft magnetic material thickness outside the HPMA is obtained to be 3% of the external radius. At this thickness, soft magnetic material is also placed inside the array as a concentrator. It is found that although using soft magnetic material inside the magnet array increases the average flux, cooling energy is decreased due to using less MCM inside the aperture because of the space occupied by the soft magnetic material.

A Novel Permanent Magnet Vernier Machine With Halbach Array Magnets in Stator Slot Opening

Permanent-magnet vernier (PMV) machines are attracting more and more attention due to their high torque density and simple mechanical structure. In this paper, a novel PMV machine with an improved permanent-magnet circuit is proposed. Compared with the regular PMV machine, half of the permanent magnets (PMs) in the rotor are moved to the stator slot opening, and Halbach array PMs are employed in the stator while the consequent pole is employed in the rotor. The analysis of this machine indicates that the back electromotive-force amplitude of the proposed PMV machine could be two times that of the regular PMV machine with similar magnet usage, and for the same torque density, viz., 23.1 kNm/m 3 , the power factor of the proposed machine can reach 0.89, while this value is only 0.65 in the regular PMV machine.

Multi-Objective Optimal Design of a Toroidally Wound Radial-Flux Halbach Permanent Magnet Array Limited Angle Torque Motor

This paper presents the modeling, optimization, and validation of a toroidally wound radial-flux Halbach array permanent magnet limited angle torque motor. A fully parameterized and flexible equivalent magnetic circuit model of the proposed motor, which is arranged in a matrix form by means of Kirchhoff's current laws for computational efficiency and ease of extension, is introduced for preliminary design. To optimize the design, a multiobjective optimization process is carried out and the multiobjective particle swarm optimization method is used to obtain the Pareto front of the desired objectives. An approved solution in Pareto front is selected and validated by finite element analysis method. A prototype based on the final design is built and tested. The experiment results further underpin the effectiveness of the proposed design and optimization approach.

Topology optimization of Halbach magnet arrays using isoparametric projection

Topology optimization using isoparametric projection for the design of permanent magnet patterns in Halbach arrays is proposed. Based on isoparametric shape functions used in the finite element analysis, the permanent magnet strength and magnetization directions in a Halbach array are simultaneously optimized for a given design goal. To achieve fabrication feasibility of a designed Halbach magnet array, two design schemes are combined with the isoparametric projection method. First, a penalization scheme is proposed for designing the permanent magnets to have discrete magnetization direction angles. Second, an extrusion scheme is proposed for the shape regularization of the permanent magnet segments. As a result, the method systematically finds the optimal permanent magnet patterns of a Halbach array considering manufacturing feasibility. In two numerical examples, a circular shaped permanent magnet Halbach array is designed to minimize the magnitude of the magnetic flux density and to maximize the upward direction magnetic flux density inside the magnet array. Logical extension of the method to the design of permanent magnet arrays in linear actuators is provided, where the design goal is to maximize the actuator magnetic force.

An Analytical Approach to Determine Coil Thickness for Magnetically Levitated Planar Motors

This paper proposes an analytical approach to directly determine coil thickness dimension only according to the magnetic pole pitch of magnetic levitation planar motors. Based on modeling of the electromagnetic forces/torques of magnetically levitated planar motors, three normalization functions about coil thickness, which are named the main forces/torques impact factor function, the y -axis attaching torque impact factor function, and the ratio factor function of the main forces/torques to coil mass, respectively, are abstracted and derived. These three normalized functions all are dimensionless and single value functions of coil thickness when magnetic pole pitch is specified. Taking the physical meanings of these three functions into account simultaneously and comparing the varying trends of these three functions synchronously, a narrower value range of coil thickness, which is between 0.318 times and 0.525 times of the magnetic pole pitch, is determined. By this approach, the coil thickness of magnetically levitated planar motors with Halbach permanent magnet array can be determined directly, instead of determining by numerical optimization usually including a few optimization parameters. This approach still allows coil thickness dimension to be fine-tuned to meet other design requirements of magnetic levitation planar motors.

Analysis and control of a 6 DOF maglev positioning system with characteristics of end-effects and eddy current damping

Magnetic levitation technology has become the great candidate to provide ultraprecision motion in vacuum environment due to its characteristics, e.g., non-contact, frictionless, and unlimited stroke, etc. This paper presents the design, modeling, analysis, and control of a 6 Degrees-Of-Freedom (DOF) maglev positioning system, and the proposed system is able to achieve a planar motion of 50 mm × 50 mm while the levitation height is up to 4 mm. In this work, the model of eddy current damping for moving Halbach Permanent Magnet (PM) array is analytically established to predict the damping force in operating of the maglev positioning system. Furthermore, the magnetic field end-effect is analyzed in the maglev system, where two guidelines are provided to ideally avoid the model error due to end-effect during the design of the maglev system. To control the maglev positioning system to achieve good planar tracking performance, the system identification is carried out for x and y-axes, and a simple PID controller is designed and optimized according to the specifications characterizing on the closed-loop performance of the maglev system. Finally, the experiments are conducted on the maglev prototype to demonstrate the positioning performance, and the results show that the maximal static positioning error is less than 200 nm with the Root Mean Square Error (RMSE) around 60 nm.

Design and Modeling of a Six-Degree-of-Freedom Magnetically Levitated Positioner Using Square Coils and 1-D Halbach Arrays

This paper presents a novel design of six-degree-of-freedom (6-DOF) magnetically levitated (maglev) positioner, where its translator and stator are implemented by four groups of 1-D Halbach permanent-magnet (PM) arrays and a set of square coils, respectively. By controlling the eight-phase square coil array underneath the Halbach PM arrays, the translator can achieve 6-DOF motion. The merits of the proposed design are mainly threefold. First, this design is potential to deliver unlimited-stroke planar motion with high power efficiency if additional coil switching system is equipped. Second, multiple translators are allowed to operate simultaneously above the same square coil stator. Third, the proposed maglev system is less complex in regard to the commutation law and the phase number of coils. Furthermore, in this paper, an analytical modeling approach is established to accurately predict the Lorentz force generated by the square coil with the 1-D Halbach PM array by considering the corner region, and the proposed modeling approach can be extended easily to apply on other coil designs such as the circular coil, etc. The proposed force model is evaluated experimentally, and the results show that the approach is accurate in both single- and multiple-coil cases. Finally, a prototype of the proposed maglev positioner is fabricated to demonstrate its 6-DOF motion ability. Experimental results show that the root-mean-square error of the implemented maglev prototype is around 50 nm in planar motion, and its velocity can achieve up to 100 mm/s.

DESIGN OF DOUBLE-SIDED LINEAR PERMANENT MAGNET EDDY CURRENT BRAKING SYSTEM

This work tries to design an Eddy current braking system that can brake at a very high speed within a short time or a short distance. In order to maximize the braking force and reduce lateral forces that can cause track deformation or damage, a double-sided linear permanent magnet Halbach array is proposed in this paper. Two possible designs (Type I and Type II) have been investigated. By using mathematic models, Finite Element Method (FEM) and experimental results, Type I design of a double-sided linear permanent magnet Halbach array is selected. Compared with the other design, Type I design can provide a much larger braking force. Moreover, the analysis also shows that the mathematic models can well capture the characteristic of Type I design. Thus these models are used to design a set of optimal design parameters such as the length and thickness of permanent magnet block to maximize flux density and braking force per unit mass of permanent magnets. The optimal performance is validated by using FEM.